Uniformly continuous homeomorphisms

✍ Scribed by O.T. Alas; A. Di Concilio

• Book ID: 104295256
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 603 KB
• Volume: 84
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00080-1

✦ Synopsis

Let (X, d) be a metric space. Under which conditions is every homeomorphism from X onto X uniformly continuous with respect to (the uniformity generated by) the metric d? We give sufficient conditions for the above question and necessary conditions for it in the case of a Odimensional homogeneous space. It is also proved that u.c.h.-ness for every compatible metric implies compactness for a nonrigid metrizable space. Furthermore, the interplay between u.c.h.ness and local m-compactness is considered in the class of uniform spaces.